How much material is wasted when a solid cone of height 24 cm and radius 8 cm is recast into a solid cylinder of radius 6 cm and height 6 cm?

cone

hieght = h = 24cm

radius = r = 8cm

volume = v = ?

v = $$\frac{\pi\times r^2\times h}{3}$$

v =$$\frac{\pi\times 8^2\times 24}{3}$$

v = $$512\pi cm^3$$

cylinder

height = h = 6cm

radius = r = 6cm

volume = ?

v = $$\pi\times r^2\times h$$

v = $$\pi\times 6^2\times 6$$

v = $$216\pi cm^2$$

wasted material

= volume of cone - volume of cylinder

= $$512\pi-216\pi$$

=  $$296\pi cm^3$$

percentage

$$512\pi : 100 :: 296\pi : x$$

$$\frac{296\pi}{512\pi}100$$ = x

296×100/512 = x

$$0.5781\times 100 = x$$

57.81 % = x

so percentage of wasted material is 57.81%